Use the definition of continuity and the properties of limits to show that the function g is continuous at a = -1. g(x) = 3x² + (x+2)5 =

Q: y-coordinate of the centroid of the plane region bounde 22 What is the y = 2x + 1, x + y = 7, and x…

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Q: Find the lateral surface of the cone generated by revolving the line y = mx from x = 0 to x = 1…

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Q: Analyze and sketch the graph of the function. Determine the critical numbers, inter- vals for which…

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Q: B. Find the area bounded by the curves, the axis and the given values of y. Sketch the graph. 3.…

A: Given problem:- B. Find the area bounded by the curves, the axis and the given values of y. Sketch…

Q: Find the area bounded by y = 2x² and y = x a. 9/2 b. 7/2 c. 5/2 d. 3/2 e. NONE OF THE ABOVE

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Q: II. Evaluate the following integrals. 2. f (sin³x)√1 + cos x dx 플

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Q: 3. Solve the differential equation of order one.  y' = csc x - ycot x STEPS: a. Put the equation…

A: Integrating factor of a differential equation of the form, dy/dx +P(x)y=Q(x) is given by, I.F=…

Q: 5(-6)+(-4)(-1)/2^2-3+(-1)

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Q: group of management students are creating a business plan for oposed shoe brand SoleSearching. The…

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Q: Find the are a of the region bounded by the given 1) sketch the area, ii) Determine the boundaries a…

A: This question can be solved using the concept of area under curves.

Q: Explain why the equation 7 = (-1,0, -1) + s(2,3,-4) + t(4,6,-8) where s, t ER does not represent the…

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Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

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Q: TU (sin³ x)√1 + cos x dx EN

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Q: Find the area of the surface generated by removing about the x-axis the upper half of the ellipse…

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Q: II. Evaluate the following integrals. 3. ²|2 - 2º| da

A: Given: ∫03|2-2x|dx

Q: Evaluate ²(2x + 3e* - 1) dx a. 12.43 b. 13.45 c. 14.24 d. 15.23 e. NONE OF THE ABOVE

A: Given problem:-

Q: 64 Lood (vt. 1 √t + √i) dt

A: Given ∫164(t-1t+t3) dtTo evaluate the Integral:

Q: 4. Find the area of the region bounded by the horizontal strip. y² +1 and the y-axis using

A: Topic = Area

Q: Solve the differential equation of order one.  (3x − 1)y′ = 6y − 10(3x − 1)1/3

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Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

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Q: What is the y-coordinate of the centroid of the plane region bounded b y = x^2 - 4 and y = 2x - x^2…

A: Y coordinates of centroid of plane is given.

Q: What is the y=x^2 4 and O 1/4 01/2 1 3/2 Ο ΝΑ x-coordinate of the centroid of the plane region…

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Q: What is the center of gravity of the solid formed when the plane region bounded by y = x^2 and y=x+2…

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Q: Find the Integrating Factor (I.F) of the following linear differential equation:

A: Please refer to the image below

Q: Determine the order of the given differential equation and state whether the equation is linear or…

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Q: Nxx X-√√x 3 olx

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Q: 3. |2 – 2" | da - 22

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Q: a. A cylindrical container that is open at the top is to be made from two kinds of material. The…

A: note : as per our company guidelines , we support one question in one request (because these two…

Q: 3. +∞ 8 -∞ dx x² + 1

A: Given ∫-∞∞dxx2+1To evaluate the integral:

Q: (y² - x² sin xy) dy+ (cos xy - xy sin xy + e²x) dx = 0

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Q: 12. We have the following width measurements of 80 meters wide lake Distance: 0 10 20 30 40 50 60 70…

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Q: 2x x→∞ 3x² +5 3x xx√√√x² x² +4 X lim x→→∞ 2 sin î (a) lim (b) lim (c)

A: Given

Q: the Using the shell method, what will be the equation of the volume of solid formed when the region…

A: Using shell method, equation of volume is given.

Q: 8. A company is selling calculators for $100 each. How many should it sell to break even if it costs…

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Q: 1. Let f(x) = sin²(x) cos(x) g(x) = sin² (x) cos² (x) h(x) = sin² (x) cos³ (x) ㅠ (a) Plot all three…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Evaluate the following integrals S- 3 • │e* − e| + (e* + = e) + e) dx e 0

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Q: II. Evaluate the following integrals. 3. 12-2² | dr

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Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

A: A particle is moving along a horizontal line such that its velocity in m/s is given by vt=2t2-16t+30…

Q: Determine the instantaneous rate of change of the function √ sin sin (2³) f(x) = [x² x3 At x=1 dt…

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Q: What is the y=x^2 - 4 and O 1/2 -1/2 3/2 -3/2 ONA y-coordinate of the centroid of the plane region…

A: Let's find y co-ordinate of the centroid of the plane bounded by two curves.

Q: 3. S x² ln xdx

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Q: Calculate the amount of money Cynthia had to deposit in an investment fund growing at an interest…

A: To find out the amount of money that Cynthia has to deposit.

Q: P 1. (1 Use the cylindrical shell method to find the volume of the solid obtained by rotating the…

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Q: 5x4y + y² 2x5 + 3xy' - dy dx O x¹y² + xy³ = 48 O x³y² + y³ = 120 о x²y² - y³ 3 = 56 O x³y² - xy³ =…

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Q: 2. Evaluate the integral: SSS teu du ds dt

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Q: 4.) Give the general solution of the following ODE: x" + 3x - 4x = 0.

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Q: Let f(x) = e2sinx 1. Find the absolute extremum values off on the interval [7]

A: To find the extreme values of given function at given  interval.

Q: For several weeks, MMDA has been recording the speed of freeway traffic in EDSA. The data suggest…

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Q: T Evaluate sec²20d0 a. 00.33 b. 0.5 c. 0.67 d. 0.25 e. NONE OF THE ABOVE O A OB O O D OE

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Q: 2. The position of a particle moving horizontally is given by s(t) = t³ − 6t² + 9t + 4, where s is…

A: s(t)=t3-6t2+9t+4   position when instance change direction means v=0…